Question

Verify the identity

cos (θ- π/2)=sinθ.

Answer 1

We use the formula
`\cos(A-B)=\cos A \cos B+\sin A \sin B`.

`\cos \left(\theta-(\pi)/(2) \right)=\cos \theta \cos (\pi)/(2)+\sin \theta \sin (\pi)/(2)`

Note that
`\cos (\pi)/(2)=0` and
`\sin (\pi)/(2)=1`.

`\therefore \cos \left(\theta-(\pi)/(2) \right)=\sin \theta`